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Abstract
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We prove an existence result for the deformed Hermitian Yang–Mills
equation for the full admissible range of the phase parameter, i.e.,
, on
compact complex three-folds conditioned on a necessary subsolution condition. Our
proof hinges on a delicate analysis of a new continuity path obtained by rewriting
the equation as a generalised Monge–Ampère equation with mixed-sign
coefficients.
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Keywords
deformed Hermitian–Yang–Mills equation, generalised
Monge–Ampère equation, special Lagrangian equation
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Mathematical Subject Classification 2010
Primary: 32Q15, 53C07
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Milestones
Received: 4 October 2019
Revised: 5 November 2020
Accepted: 31 December 2020
Published: 3 September 2022
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